A parallel manipulator is a device having a base and a platform interconnected by at least three independent connections each of which is variable in length and is mounted to the base and platform, in a way in which provides six degrees of freedom. In a hexapod there are six independent connections pivotally mounted to the base and platform. Thus, by varying the relative lengths of the connections, the orientation and position of the platform relative to the base may be varied. A Stewart platform, whose six degrees of freedom can be exercised by varying the length of the actuators, is known as a Generalised Stewart Platform (GSP), and sometimes as a Stewart-Gough Platform. Examples of such GSPs are disclosed in U.S. Pat. No. 5,728,095 and WO 99/28095. In those examples, the base and platform are linked by six actuators. Moreover, since the base and platform may be symmetric, it becomes a matter of choice as to which is which, the base being the component from which the position and orientation of the platform is determined. The base and platform can be of any geometry.
The GSP has been put into effect in the form of the Taylor Spatial Frame (TSF), to act as an orthopaedic fixator. It is a parallel manipulator with a full set of six degrees of correctional freedom; this is illustrated in detail in e.g. U.S. Pat. No. 5,728,095 referred to above. In such a Taylor Spatial Frame, the links are in the form of actuators, which are inclined to the perpendicular between the base and the platform, with adjacent actuators inclined in opposite directions so as to form an approximately cylindrical structure.
It is a relatively straightforward matter to determine the length of the connections that are needed when the locations and orientations of the base and platform are known, but it is amore difficult problem to determine the position and orientation of the platform given the lengths of the links. Since it is the links that are controllable in length, e.g. because they are actuators controlled by an operator, a user of a Taylor Spatial Frame must have a way of determining the platform position and orientation given control actions, or given variations in the lengths of the links. For a given set of link lengths, equations can be set up to enable the position of the platform to be determined relative to the base, but such equations are not easy to solve. In practice, numerical methods, based on iterative schemes, have been found to be more useful than attempts to find the solution by algebraic methods. Algebraic methods may lead to all known solutions, but for practical control operations only one solution is needed.
However, known numerical methods for determining the position of the platform relative to the base have tended to involve long processing times, making their use for practical applications, such as in orthopaedics, inappropriate. For such arrangements, a substantially real-time solution is needed, and known arrangements have not been able to provide this.